Light scattering by epitaxial VO2 films near the metal-insulator transition pointSergiy Lysenko, Felix Fernández, Armando Rúa, Joaquin Aparicio, Nelson Sepúlveda, Jose Figueroa, KevinVargas, and Joseph Cordero Citation: Journal of Applied Physics 117, 184304 (2015); doi: 10.1063/1.4921057 View online: http://dx.doi.org/10.1063/1.4921057 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/117/18?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Improved metal-insulator-transition characteristics of ultrathin VO2 epitaxial films by optimized surfacepreparation of rutile TiO2 substrates Appl. Phys. Lett. 104, 081918 (2014); 10.1063/1.4866037 Comprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO2 thin films J. Appl. Phys. 113, 043707 (2013); 10.1063/1.4788804 Evolution of local work function in epitaxial VO2 thin films spanning the metal-insulator transition Appl. Phys. Lett. 101, 191605 (2012); 10.1063/1.4766292 Increased metal-insulator transition temperatures in epitaxial thin films of V 2 O 3 prepared in reduced oxygenenvironments Appl. Phys. Lett. 98, 152105 (2011); 10.1063/1.3574910 Metal-insulator transition in epitaxial V 1 − x W x O 2 ( 0 ≤ x ≤ 0.33 ) thin films Appl. Phys. Lett. 96, 022102 (2010); 10.1063/1.3291053

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Light scattering by epitaxial VO2 films near the metal-insulator transitionpoint

Sergiy Lysenko,1,a) Felix Fern�andez,1 Armando R�ua,1 Joaquin Aparicio,2

Nelson Sep�ulveda,3 Jose Figueroa,1 Kevin Vargas,1 and Joseph Cordero1

1Department of Physics, University of Puerto Rico, Mayaguez, Puerto Rico 00681, USA2Department of Physics, University of Puerto Rico-Ponce, Ponce, Puerto Rico 00732, USA3Department of Electrical and Computer Engineering, Michigan State University, East Lansing,Michigan 48824, USA

(Received 15 February 2015; accepted 1 May 2015; published online 14 May 2015)

Experimental observation of metal-insulator transition in epitaxial films of vanadium dioxide is

reported. Hemispherical angle-resolved light scattering technique is applied for statistical analysis

of the phase transition processes on mesoscale. It is shown that the thermal hysteresis strongly

depends on spatial frequency of surface irregularities. The transformation of scattering indicatrix

depends on sample morphology and is principally different for the thin films with higher internal

elastic strain and for the thicker films where this strain is suppressed by introduction of misfit dislo-

cations. The evolution of scattering indicatrix, fractal dimension, surface power spectral density,

and surface autocorrelation function demonstrates distinctive behavior which elucidates the influ-

ence of structural defects and strain on thermal hysteresis, twinning of microcrystallites, and do-

main formation during the phase transition. VC 2015 AIP Publishing LLC.

[http://dx.doi.org/10.1063/1.4921057]

INTRODUCTION

Metal-Insulator transition phenomenon in vanadium diox-

ide receives much attention since Morin’s discovery.1 VO2

shows unique transformation of structural, electronic, and opti-

cal properties above room temperature, at Tc’ 340 K.1–8 Upon

heating, VO2 undergoes a first-order insulator-to-metal phase

transition (PT) with reversible change of monoclinic symmetry

to tetragonal one. A number of studies were focused on size-

dependent transition in isolated nanoparticles and film grains

due to importance of fundamental processes involved in the

PT dynamics and prospective technological use of VO2-based

materials.9–15 The observations of spatially resolved PT in

VO2 at the nanoscale level were recently reported in several

papers, which demonstrate noticeable size-dependent transition

dynamics in nanoparticles and nanocrystalline films.16–21

Despite significant effort in experimental and theoretical

study of VO2, the problem related to the PT mechanism in

this material is still far from complete understanding owing

to variety of discrepant experimental data. Slight variations

in sample morphology and stoichiometry result in consider-

able change of elastic, electronic, and optical properties near

the critical point. While studies of PT in single-crystal nano-

beams, nanorods, and nanoplatelets usually provide most

reproducible data, the information about PT dynamics in epi-

taxial and polycrystalline VO2 films is quite fragmentary. At

the same time, the understanding of structural dynamics in

thin films is of special interest, since different films represent

stochastic or highly ordered model systems with different

morphology and concentration of structural defects. It was

shown recently22–24 that the stress and strain in VO2 film sig-

nificantly depend on film thickness, grain size, and substrate.

The new information about multi-scale structural PT and do-

main formation can bring better understanding of different

physical processes near the PT point of VO2.

In this paper, we demonstrate the influence of internal

strain and morphology of epitaxial VO2 films on thermally

induced domain formation and PT dynamics at different spatial

scales. Angle-resolved measurements of elastic light scattering

were performed to obtain the power spectral density (PSD),

fractal dimension, and autocorrelation function (ACF) of the

surface near Tc. It is shown that the size and shape of hystere-

sis loop depend on surface spatial frequency due to grain-size-

dependent elastic strain and/or concentration of structural

defects. The thermal evolution of scattering pattern and surface

morphology of strained continuous film is found considerably

different as compared to the film with overcritical thickness,

where strain is relaxed via misfit dislocations (MDs). We find

that the internal elastic strain in thin VO2 film is the main ori-

gin which affects scattering indicatrix, producing twinning of

microcrystallites and domain formation during PT.

EXPERIMENTAL

The pulsed laser deposition (PLD) technique was

applied to fabricate a set of VO2 films on single-crystal

(012)Al2O3 (r-cut) and (001)Al2O3 (c-cut) sapphire sub-

strates. The ablation of metallic vanadium target was per-

formed by excimer laser (Lambda Physik Compex 110) with

wavelength k¼ 248 nm (KrF excimer), 10-ns pulse duration,

and 4 J/cm2 fluence, and a chamber atmosphere of O2 and Ar

at 30 mTorr pressure. Gases were injected into chamber

through separated mass flow controllers with 20:5 (O2:Ar,

cm3/min:cm3/min) flow rate. The X-ray diffraction patterns

of all VO2 films evidenced single monoclinic M1–phase at

room temperature.a)Electronic mail: sergiy.lysenko@upr.edu

0021-8979/2015/117(18)/184304/11/$30.00 VC 2015 AIP Publishing LLC117, 184304-1

JOURNAL OF APPLIED PHYSICS 117, 184304 (2015)

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Several laser sources were employed to study the ther-

mally induced PT in VO2. A continuous wave 8 mW semi-

conductor laser with wavelength k¼ 1310 nm was used in

optical transmission measurements, and a 2 mW He-Ne laser

with k¼ 632.8 nm was used as a probe light source in the

light scattering experiment. The sample temperature was

controlled by a Peltier heater.

The observation of light scattering was conducted with a

scatterometer described elsewhere.25,26 This apparatus pro-

vided measurements of bidirectional-scatter-distribution-

function

BSDF h;uð Þ ¼ dIscatt h;uð ÞdX

� �1

I0 cos h; (1)

where h and u are the polar and azimuthal scattering angles,

respectively. I0 is the intensity of incident light, dIscatt is the

intensity of light scattered into solid angle dX.

Angle-resolved elastic light scattering is a powerful

technique for statistical analysis of surface irregularities of

different sizes.27–33 While this technique does not provide

real-space imaging of the surface roughness or VO2 domains,

it produces direct reciprocal-space imaging with robust statis-

tical information about distribution of the inhomogeneities.

Any type of structural ordering on the mesoscale, self-

organization, twinning of microcrystals, and domain forma-

tion produces sharp diffraction peaks or symmetric features

(e.g., lines, rings, squares, rhombs, hexagons, etc.) in the

scattering indicatrix. Complex evolution of the structure on

different scales can be easily identified and monitored by

measuring the scattering signal at certain angles.

In this work, the measured BSDF data were used for cal-

culation of two-dimensional (2D) power spectral density

function of the surface as

PSDsð~f Þ ¼ BSDFð~f Þ=OF; (2)

where OF is an optical factor which depends on dielectric

permittivity and scattering angle.33 OF was calculated using

equations obtained by Elson in Ref. 34. The optical constants

for these calculations were obtained from additional angular

measurements of reflection coefficient and data fit for s- and

p-polarization of incident light. The PSD(f) function repre-

sents the statistical distribution of surface roughness versus

surface spatial frequency f¼ sin h/k and is the Fourier trans-

form of the surface autocorrelation function ACF(r).

The autocorrelation function defines correlation of sur-

face irregularities versus the translation length r in the surface

plane.33 At zero translation ACF(0)¼ d2, where d is rms

roughness. In this work, we use the normalized autocorrela-

tion functions ACF/d2, calculated from scattering (ACFs) and

atomic-force-microscopy data (ACFAFM), where ACFs(0)¼ 1

and ACFAFMð0Þ ¼ 1.

There are several instrumentation-dependent limitations

to observe the structural dynamics by elastic light scattering

such as wavelength and light polarization, angle of inci-

dence, aberration of the optical system, and resolution of the

charge-coupled device (CCD). The light scattering experi-

ment depends on a significant number of different

parameters, and some of them can be unknown. The range of

spatial frequencies available for observation is limited by the

probe wavelength. In this work, the measurements were per-

formed at normal incidence. The light scattered at h¼ 90�

corresponds to the maximal spatial frequency available for

observation, fmax¼ sin 90�/k¼ 1/k. The central part of the

scattering indicatrix is blocked by the sample holder, which

prevents measurement of the signal for low spatial frequen-

cies �0.4 lm�1.

The Raman effect was measured in backscattering con-

figuration from room temperature to 400 K by a Renishaw

Raman Microspectrometer RM2000 system. The instrument

was equipped with a CCD detector, Leica microscope, and a

diode laser with wavelength k¼ 532 nm.

The VO2 film surface was also scanned by atomic-force-

microscope (AFM, Park Scientific Instruments, Autoprobe

CP). The AFM topography analysis, calculation of spectral

density, and autocorrelation function of the surface rough-

ness were performed with WSxM software.35

RESULTS AND DISCUSSION

Surface morphology and domain formation

The distribution and orientation of crystalline domains in

thin ferroelastic VO2 film strongly depend on the strain field

and correspond to the minimum of elastic energy. Self-

organization of VO2 domains is a complex problem related to

the misfit strain �m between film and substrate, defects, and

interference of strain fields from different crystallites. The

influence of the substrate on the net strain is crucial. Thus,

the parallel ordering of ferroelastic microcrystals in most

cases reduces the long-order strain field,36 as observed for

nanoplatelets,16,21,37,38 nanobeams,39 and for epitaxial VO2

films on TiO240 and Al2O3 single-crystal substrates.24,41–45

The r-cut sapphire substrate Al2O3 is characterized by a rec-

tangular atomic lattice on the surface, and the VO2 PLD

film is strongly oriented on this substrate with directions

½010�VO2k½100�Al2O3 and ½001�VO2k½02�1�Al2O3. Some of these

directions can be slightly misoriented within less than 1�.25

Such a small misorientation is likely due to elastic interaction

between different crystallites, defects and substrate.

The BSDF indicatrices of hemispherical light scattering

are shown in Fig. 1(a) for 30-nm-thick VO2/Al2O3(r-cut)

film as a function of both polar h and azimuthal u angles. A

distinctive feature of these indicatrices is a square-like pat-

tern outlined by isophotes in the central area within 0�< h� 55�. The isophotes are parallel to [010] (bm) and [001]

(cm) directions of the epitaxial VO2 film. At larger polar

angles, this pattern loses its sharpness. A slight elongation of

isophotes along u ¼ 90�, 270� direction is due to intrinsic

polarization anisotropy of the scattering process, since the

polarization of incident light was oriented along this azi-

muthal direction. The power spectral density function PSDs

of the surface calculated from scattering indicatrix eliminates

such polarization anisotropy [Fig. 1(b)]. Nevertheless, the

square-like pattern remains in the center of the PSDs map

and is a signature of highly ordered domains in the film.

The texture of epitaxial films is highly influenced by the

substrate and film thickness. In order to demonstrate this

184304-2 Lysenko et al. J. Appl. Phys. 117, 184304 (2015)

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influence, we show several scattering indicatrices obtained

for VO2 films deposited on c-cut Al2O3 (Fig. 2), which are

considerably different as compared to indicatrices for VO2/

Al2O3(r-cut). In a series of previous XRD studies,24,42–44,46 it

has been shown that the VO2/Al2O3(c-cut) film undergoes

3-fold twinning. These films are highly textured with orienta-

tion of ½100�VO2 domain axis along three equivalent crystallo-

graphic directions of Al2O3(c-cut) substrate. As a result, for

uniformly twinned 50-nm-thick VO2/Al2O3(c-cut) film the

indicatrices show symmetric directions of scattering with

60� angular separation [Fig. 2(a)]. The local twinning of

some films can produce more complex texture with rotation

of domains by the angles other than 60�.42,47 Thus, the indi-

catrices for 30-nm-thick VO2/Al2O3(c-cut) show the prefer-

ential directions of scattering with 45� and 75� angular

separation [Fig. 2(b)]. This indicates the presence of domains

rotated by 45� and 75�. The specific domain formation in

VO2/Al2O3(c-cut) makes these films optically isotropic,

while the films deposited on Al2O3(r-cut) retain their optical

properties inherent to VO2 single crystal.42 The local mor-

phology of VO2/Al2O3(r-cut) was found to be more uniform

within the sample, as compared to VO2/Al2O3(c-cut), and

further discussion will be focused on optical properties of

VO2/Al2O3(r-cut).

The AFM data for 30-nm-thick VO2/Al2O3(r-cut) films

yield the rms roughness of the surface as d¼ 96 A. Fig. 3(a)

FIG. 1. (a) Temperature-dependent evolution of light scattering indicatrix for 30-nm-thick film VO2/Al2O3(r-cut). Arrow marks a square-like pattern at

T¼ 296 K. (b) Power spectral density of the surface at T¼ 296 K. Central and periphery region of PSD map was reconstructed using the Gerchberg-Saxton ER

algorithm. Dashed isophotes outline the square-like pattern. (Multimedia view) [URL: http://dx.doi.org/10.1063/1.4921057.1]

FIG. 2. The light scattering from VO2/Al2O3(c-cut) films. (a) log(BSDF) for

50-nm-thick film in insulating (T¼ 303 K) and metallic (T¼ 358 K) state. (b)

log(BSDF) for different areas of 30-nm-thick film obtained with k¼ 400 nm

laser wavelength. Dashed lines indicate preferential directions of scattering.

FIG. 3. Morphology of 30-nm-thick film VO2/Al2O3(r-cut). (a) 2� 2 lm2

AFM topography and (b) 2� 2 lm2 surface autocorrelation function

ACFAFM. Periodical fringes are marked by dashed lines. (c) Power spectrum

extracted from AFM and light scattering data at T¼ 296 K. Dashed lines are

fit by Eq. (3). The inset shows a cross-section of 2D ACFAFM.

184304-3 Lysenko et al. J. Appl. Phys. 117, 184304 (2015)

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shows that the lateral shape of VO2 grains is somewhat rec-

tangular, similar to nanorods studied by Sohn et al.48 and

Kim et al.49 The average lateral size of VO2 grains is dav

’ 305 nm, which corresponds to spatial frequency fg¼ 1/

dav¼ 3.3 lm�1. This range is unattainable in the scattering

measurements since the maximal spatial frequency probed

by the He-Ne laser is fmax¼ 1/k¼ 1.58 lm�1. However, the

square-like pattern in the scattering indicatrix at h< 55�

(f< 1.3 lm�1) indicates that the VO2 crystallites are organ-

ized into highly ordered clusters. Above h¼ 55�, this pattern

is distorted and less pronounced owing to increased random-

ness in orientation of smaller surface irregularities.

The 2D autocorrelation function of surface roughness

calculated from AFM topography [Fig. 3(b)] shows a pres-

ence of isotropic and weak anisotropic components. The iso-

tropic component of surface roughness contributes only in

the central maximum of ACFAFM with near-exponential

decay within �300 nm [inset in Fig. 3(c)] and, therefore, can

be easily separated from the rest of ACFAFM. A periodical

anisotropic component results in the oscillation of ACFAFM,

showing fringes with period of 0.55 lm. This indicates an

ordering of microstructure along the fringe direction.

Taking into account AFM data, the observed indicatrices

in Fig. 1 can be characterized in terms of fractal surface scat-

tering where the scattered field contains information about sub-

wavelength VO2 crystallites organized in highly ordered

square-like structures due to anisotropic ordering on the single-

crystal r-cut sapphire substrate. The structure of epitaxial VO2/

Al2O3 films is a classic example of a “supercrystal,” where

the groups of nanocrystals are organized in polysynthetic

domains.36 In contrast to a single-crystal, the “supercrystal”

film is a quite flexible structure with relatively high mechanical

mobility of nanocrystals. Thus, a small change in the elastic

energy results in splitting of the film into domains of the same

or different phases in order to reduce the net elastic energy.36,50

This is an intrinsic property of thin VO2 films which qualita-

tively changes the temperature-dependent scattering pattern in

Fig. 1(a).

The information about fractal properties of the sample

was obtained from the power spectra PSDAFM and PSDs

calculated from AFM topography and scattering data,

respectively. It is noted that the data obtained from AFM

and from elastic light scattering cover different ranges of

spatial frequencies. Moreover, these experimental techni-

ques are based on different physical processes of interaction

between the probe (i.e., light or AFM tip) and the surface.

The comparison of PSDs and PSDAFM functions shows their

overlap [Fig. 3(c)]. Also, the slope of PSDAFM within

f¼ 1.4–3.0 lm�1 coincides with the slope of PSDs function.

This indicates that the AFM and light scattering measure-

ments yield the same information about fractal dimension

of the surface. At lower spatial frequencies f< 1.3 lm�1,

the PSDAFM function has only few data points, and within

this range the accuracy of AFM measurement is slightly

lower as compared to higher frequencies. Since the AFM is

a conventional and precise tool to characterize surface

roughness, the overlap between PSDs and PSDAFM data

denotes a high precision of scattering measurements.

Both PSD functions show fractal-like behavior and can

be characterized by 2D power spectrum51

PSD fð Þ ¼C nþ 1ð Þ=2� �

2C 1=2ð ÞC n=2ð Þ �Kn

f nþ1; (3)

where the Kn and n are constants. The Hausdorff-Besicovitch

dimension is defined as D¼ (5� n)/2 and, along with Kn and

n, is the fractal parameter of surface inhomogeneity.51–53

The PSDs functions at different azimuthal angles u show

the same slope in a log� log graph [Fig. 3(c)], indicating a

relatively high isotropic component of surface roughness.

Applying the fractal approach for analysis of surface rough-

ness, one can expect the independence of the fractal parame-

ters on experimental bandwidth. However, the fitting of PSD

data with Eq. (3) shows some difference. The parameters

obtained for PSDs are n¼ 1 (D¼ 2), while the PSDAFM

shows multifractal behavior and can be described by a sum of

PSD functions with n¼ 2.75 (D¼ 1.13) at f¼ 3.3–30 lm�1

and n¼ 1 (D¼ 2) at f> 30 lm�1 and f¼ 1.4–3.0 lm�1. It is

important to note that the lower limit of the linear part of

PSDAFM with n¼ 2.75 coincides with the spatial frequency of

VO2 crystallites fg¼ 3.3 lm�1. Moreover, the fractal parame-

ters of PSDs coincide with those of PSDAFM at f> 30 lm�1

and f¼ 1.4–3.0 lm�1.

The PSD data in Fig. 3(c) reveal the multifractal struc-

ture of the film. The distribution of small VO2 irregularities

with f> 30 lm�1 likely replicates the Al2O3 substrate rough-

ness. The obtained fractal dimension D¼ 2 (n¼ 1) corre-

sponds to the extreme fractal and indicates close-packed

crystallites of rugged surface.52,53 The distribution of larger

VO2 grains with fg< f< 30 lm�1 is organized into another

fractal structure with D¼ 1.13 (n¼ 2.75) related to smoother

surface. However at f< fg the VO2 irregularities again are

organized in domains with D¼ 2 (n¼ 1), as at f> 30 lm�1.

The averaged power spectra PSDs calculated for 30-nm-

thick film in insulating and metallic state show a noticeable

difference in slope (see inset in Fig. 4(a)). The fractal dimen-

sion decreases from D¼ 2 (n¼ 1) to D¼ 1.85 (n¼ 1.3) dur-

ing the PT, indicating a smoothing of surface irregularities in

the metallic phase.

In terms of Rayleigh smooth-surface criterion,33 the epi-

taxial VO2 film with d< k/(4p) can be considered as opti-

cally smooth. For such surface the BSDF(f) is nearly scaled

PSD function, as depicted in Fig. 4(a) for the cross-section

of the scattering indicatrix at u ¼ 0�, T¼ 296 K. Therefore,

correct information about statistical distribution of surface

inhomogeneities can be obtained directly from BSDF data.

This is “scatter prediction” method that allows reconstruct-

ing the evolution of surface irregularities when the system is

in nonequilibrium or quasi-equilibrium state, and material

optical constants are unknown.

The distinctive feature of BSDF(h), BSDF(f), and

PSDs(f) for VO2/Al2O3 is a presence of sharp peaks, as iden-

tified in Figs. 1 and 4. This is the typical signature of strong

ordering of crystallites along different directions. The self-

organized surface structures scatter light as differently ori-

ented diffraction gratings whose period depends on film

temperature. Thus, the BSDF undergoes noticeable change

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with temperature (Figs. 1 and 4). During the PT most diffrac-

tion peaks are shifting, emerging, or decaying due to twin-

ning of VO2 microcrystallites accompanied by “dynamic”

domain formation process. Moreover, the evolution of scat-

tering pattern begins well below the critical temperature Tc

and persists well above it.

The emergence of new diffraction peaks can be

observed in Fig. 4(b) at higher spatial frequencies above

f¼ 1.2 lm�1 already at T¼ 308 K. This figure indicates

an isotropic formation of domains with sizes less than

d¼ 1/f¼ 0.83 lm. As the temperature reaches T¼ 328 K, the

region affected by the PT uniformly spreads to f¼ 0.9 lm�1

(d¼ 1/f ¼ 1.1 lm). With further temperature increase, new

diffraction peaks uniformly fill up all scattering indicatrix.

This temperature-dependent process corresponds to the

realignment of domains and significantly varies from sample

to sample. The self-organized surface structure consists of

parallel-sided VO2 domains with period dD ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2cH=eS

p,

where c is the specific surface energy of the domain bound-

ary, H is the film thickness, and eS is the specific surface

energy of local deformations at the boundary between film

and substrate.36,54 The spatial frequency of this structure is

fD ¼ffiffiffiffiffiffiffiffiffieS

2cH

r: (4)

Since fD �ffiffiffiffiffiffiffiffiffieS=c

p, a small change in the internal strain of

the film or nucleation of new phase both result in the forma-

tion of new domain pattern, affecting the scattering

indicatrix.

For 30-nm-thick VO2/Al2O3(r-cut), the change in scat-

tering indicatrix starts at room temperature, immediately

when heating is applied. The arbitrary cross-section of the

indicatrix at T¼ 333 K shows sharp peaks at f� 0.6 lm�1

[f¼ 0.59 lm�1 in Fig. 4(a)] which are assigned to strong

ordering of VO2 domains with a period of d¼ 1.7 lm. At

the PT temperature Tc¼ 341 K, the structural inhomogene-

ity of the film becomes highest due to coexistence of differ-

ent phases. The sharpness of the square-like pattern in the

center of scattering indicatrix in Fig. 1 decreases. When the

temperature reaches T¼ 365 K, the VO2 has completely

switched into its metallic R-phase and the new set of quasi-

periodic diffraction peaks appears [starting at f¼ 0.53 lm�1

in Fig. 4(a)]. This behavior corresponds to self-organization

of domains in new periodic structures with minimal elastic

energy.

Additional information about evolution of VO2 structure

was obtained from the autocorrelation function ACFs calcu-

lated by Fourier transform of PSDs(f) and BSDF(f) using the

Gerchberg-Saxton error reduction (ER) algorithm which sig-

nificantly reduces numerical error.26,55,56 This algorithm was

also applied to restore absent PSDs(f) data at the periphery

up to f¼ 2.1 lm�1 and in the central area of the scattering

indicatrix blocked by the sample holder [Fig. 1(b)]. At some

temperatures, the calculation of PSDs was not performed,

because of lack of information about VO2 optical constants

near the PT point. Therefore, ACFs were calculated from

BSDF data instead of PSDs, since BSDF(f) is practically a

scaled PSDs(f) for a smooth surface, as discussed above and

shown in Fig. 4(a).

Fig. 5(a) shows the ACFs distribution for insulating and

metallic phases versus translation length. The distinctive fea-

ture of ACFs is a presence of spatial oscillations with or-

dered maxima due to domain formation in the epitaxial film.

In insulating phase the nodded-type maxima are aligned in a

mesh marked by dashed lines in Fig. 5(a), separated by

2.2 lm. This structure of ACFs is very similar to fringes of

ACFAFM separated by 0.55 lm [Fig. 3(b)]. It is very likely

that the ACFs represents the same highly ordered domains as

ACFAFM but with filtered out higher spatial harmonics, since

the experimental bandwidths of AFM and light scattering

experiments are substantially different.

The measure of surface inhomogeneity can be refer-

enced to the autocorrelation length (ACL) of the surface.

ACL is defined as the ACF halfwidth at the ACF(0)/e point,

FIG. 4. The evolution of scattering pattern and power spectral density of the

surface roughness for 30-nm-thick film VO2/Al2O3(r-cut). (a) Cross-sections

of the BSDF scattering indicatrix and PSDs at u ¼ 0�. Inset shows the azi-

muthally averaged PSDs function for insulating and metallic phases. Dashed

lines are fit by Eq. (3). (b) The relative change DBSDF(T)/BSDF0 near the

PT point, where BSDF0 is obtained for insulating VO2 at T¼ 296 K, and

DBSDF(T)¼BSDF(T) � BSDF0. Arrows mark the region that corresponds

to the noticeable emergence of new diffraction peaks.

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and related to the uniform isotropic component of roughness

and calculated from the central peak of ACF map. The dif-

ference in experimental bandwidth results in different values

of ACL obtained by different techniques. Thus, the autocor-

relation length ACLAFM ¼ 100 nm [inset in Fig. 3(c)]

derived from AFM measurements is almost five times less

than ACLs¼ 595 nm calculated from scattering data at

T¼ 296 K [see inset in Fig. 5(b)]. As the temperature

increases, the ACLs decreases and reaches a 529 nm mini-

mum at PT critical point Tc¼ 341 K. This indicates a gradual

increase of disorder in the VO2 film. However, after the PT

at T¼ 353 K, the order significantly increases and the ACLs

recovers to 574 nm. The noded maxima of ACFs [Fig. 5(a)]

migrate during the heating process and in the metallic phase

they become more pronounced [see inset in Fig. 5(b)]. Their

locations at T¼ 353 K are not strictly aligned in a mesh as at

T¼ 296 K, and in vertical direction [Fig. 5(a)] the average

separation between maxima at T¼ 353 K shrinks to 1.8 lm,

indicating noticeable surface reconstruction.

There are two origins for surface scattering: inhomoge-

neity of the dielectric permittivity e and geometrical rough-

ness. Since below the PT point there are no metallic nuclei

which could provide significant disorder in dielectric con-

stant, it is difficult to assign the observed significant change

of ACFs, BSDF, and shift of diffraction peaks in Figs. 1(a)

and 4 to scattering from temperature-dependent inhomogene-

ity of e. The Raman scattering experiment conducted by

Atkin et al.57 has shown that the intermediate M2-phase

can nucleate in strained VO2 at temperatures below Tc.

However, nucleation of M2-phase during the heating process

would not add noticeable disorder in e either, since the

dielectric constants of M1 and M2 phases are almost indistin-

guishable within the optical region. On the other hand, new

M2-phase at the nanoscale can certainly change the strain

field of polydomain VO2 film and, as a result, can introduce

further domain formation and new elastic deformations.

In this work, Raman scattering was measured at differ-

ent temperatures of the film in order to verify the presence

of M2-phase. Fig. 6 shows Raman spectra of stoichiometric

VO2 at different temperatures. As shown in Refs. 57–59, the

distinctive signature of M2 and T-phase in strained sample is

splitting and blueshifting of the Ag 613 cm�1 phonon mode

as well as decay of the low-frequency mode Ag 194 cm�1.

Nevertheless, the Raman spectra in Fig. 6 do not show such

behavior, indicating absence or low concentration of M2-

phase at room temperature and near the PT point Tc. While

even a small concentration of M2-phase can affect the net

strain field, another origin of elastic strain in the film is a dif-

ference in thermal expansion of VO2 (5.78� 10�6 K�1 at

298–334 K and 13.35� 10�6 K�1 at 339–360 K)60 and

Al2O3 substrate (8� 10�6 K�1).61 This can produce a notice-

able change in the strain field of the epitaxial film when the

temperature changes by several degrees.

Taking into account Eq. (4) along with Raman scattering

and thermal expansion data, the observed continuous evolu-

tion of BSDF within broad temperatures outside the PT

range (Figs. 1 and 4) is assigned to domain formation and

elastic deformation of the film due to strain effects. It is very

likely that in the 30-nm-thick VO2/Al2O3 the elastic strain,

particularly misfit strain, is not relaxed via formation of

static dislocation network. Instead, the strain relaxation is

accompanied by “dynamic” temperature-dependent forma-

tion of twins, presumably oriented at �45� angle to the sub-

strate as observed by Zhao et al.43 for VO2/Al2O3(r-cut)

epitaxial film.

The conclusion about the presence of significant internal

strain in thin VO2 film is in agreement with data obtained in

Ref. 22, where the absolute value of residual stress was

found to be higher for thinner films. It was shown that the re-

sidual stress for the 100-nm-thick VO2 film deposited on Si

substrate by radio frequency (RF) sputtering is �677 MPa,

FIG. 5. (a) Autocorrelation function of VO2 surface for insulating M1-

phase (T¼ 296 K) and metallic R-phase (T¼ 353 K). (b) Cross-section of

ACFs distribution at different temperatures. Upper inset shows oscillatory

component of ACFs. Lower inset shows evolution of autocorrelation length

versus temperature. (Multimedia view) [URL: http://dx.doi.org/10.1063/

1.4921057.2]

FIG. 6. Raman spectra of VO2 at different temperatures.

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and it changes to �73 MPa as the thickness increases to

440 nm. Moreover, the PT produces additional alteration of

the stress. For PLD films grown on single-crystal Al2O3

(r-cut) substrate the absolute value of internal stress is cer-

tainly different and is expected to be higher due to epitaxial

nature of the film.

The structure of epitaxial film remains continuous on the

microscopic level upon full cycle of the PT process due to

phase coherency. This coherency is attained by relaxation of

structural strain via microdeformations at the grain boundaries

and at the boundary which separates different VO2 phases and

domains. The strain energy is transferred into energy of struc-

tural microdeformations and/or defects.62 Suppressing the

long-order macroscopic strain field in the epitaxial film, the

microdeformations are non-coherent with the net strain field

and are a residual origin of the strain. Therefore, the strain-

assisted domain formation in the film starts mostly within the

microdeformations. That is, at the boundary of neighboring

grains or phases and at structural defects.

The angle-resolved light scattering technique provides

direct statistical imaging of multi-scale grain-size-dependent

transitions in the film. The thermal hysteresis of scattering

signal for structures with different spatial frequencies f is

shown in Fig. 7. We note that the smaller structures with

higher spatial frequencies scatter light less and their contri-

bution is almost hidden in the total scattering signal Iscatt/I0

integrated within hemisphere. Therefore Fig. 7(a) shows nor-

malized graphs of scattering signal I�scatt for different f, where

I�scatt ¼ 1 corresponds to insulating and I�scatt ¼ 0 to metallic

phase. In order to define the point of steepest slope of the

hysteresis, dI�scatt=dT derivatives were calculated. Here, the

thermal range between minima of dI�scatt=dT curves is defined

as a characteristic width DT of the hysteresis. Thus, Fig. 7(b)

shows the same DT¼ 3.5 K for structures with different spa-

tial frequencies. Nevertheless, the hysteresis is different for

different structures: it noticeably broadens at higher spatial

frequencies. This broadening is assigned to stronger misfit

strain and higher concentration of structural defects in

smaller grains.10,11,63

Other important aspects which can be monitored by light

scattering are fluctuations of density and entropy due to

defects, strains, and coexistence of insulator and metallic

phases near the critical point.64 These factors increase fluctua-

tion of the dielectric constant e as the temperature approaches

the PT point and, as a consequence, increase the scattering sig-

nal. This appears as a sharp rise of the scattering [dashed por-

tion in Fig. 7(a)], and referenced as “transition opalescence.”65

It is remarkable that such a scattering feature is more pro-

nounced and broader for smaller grains. This result proves the

heretofore debatable opinion that the smallest VO2 grains are

under relatively high and random local elastic strains from the

substrate and neighbouring grains, and can contain larger

number of oxygen vacancy defects which provide significant

system disorder at the critical point.

Influence of the film thickness on structuraltransformation of the film

It was found that the increase of the film thickness above

some critical value results in noticeable changes of scattering

and hysteresis properties. Thus, the integrated scattering in-

tensity for 125-nm-thick PLD film is increased by a factor of

two with respect to the 30-nm-thick film, indicating increased

surface roughness by a factor of �ffiffiffi2p

.33 The distribution of

VO2 crystallites in the thicker film has a higher degree of iso-

tropy, resulting in almost complete blurring of the rectangular

shape of isophotes in Fig. 8(a), particularly at higher spatial

frequencies. Nevertheless, this distribution is not random and

forms strongly ordered groups of crystallites.

The cross-section of the scattering indicatrix along

an arbitrary direction shows equidistant BSDF(f) maxima

[Fig. 8(b)]. Thus, separation of BSDF(f) peaks for azimuthal

directions u ¼ 47� is Df¼ 8.7� 10�2 lm�1. The BSDF(f)with equidistant maxima is related to corrugated surface

relief and can be modeled by superposition of light scattering

from a diffraction grating of several lines superimposed onto

a stochastic surface relief. The modeling of BSDF(f) using

the equation for the intensity of light diffraction by periodi-

cal structures66,67

IDG ¼ ID0

sin Npdfð Þsin pdfð Þ

� �2sin psfð Þ

psf

� �2

; (5)

shows good coincidence with experimental data when the

diffraction grating consists of N¼ 3 lines with period

d¼ 12 lm, separated by boundaries with width s¼ 0.61 lm.

Here, ID0 is maximal diffraction intensity. The location of the

FIG. 7. (a) Hysteretic evolution of VO2 scattering signal for integrated light

scattering and for scattering by different spatial frequencies of the surface.

(b) Derivative of normalized scattering intensity. Starting points of the PT

for spatial frequencies f1¼ 0.6 lm�1, f2¼ 1 lm�1, and f3¼ 1.54 lm�1 are

marked as S1, S2, and S3, correspondingly.

184304-7 Lysenko et al. J. Appl. Phys. 117, 184304 (2015)

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equidistant diffraction peaks IDG, their separation DfDG¼ 8.3

� 10�2 lm�1, as well as presence and positions of minor dif-

fraction peaks are very close to those in the experimental

BSDF(f) data [Fig. 8(b)]. This model assumes that the VO2

crystallites organize as relatively large ordered 12 lm

domains, separated by a 0.61 lm boundary formed by one or

two crystallites. Moreover, since epitaxial VO2 film can be

considered as a “supercrystal,” as discussed above, it is

expected that the large 12 lm domains also contain ordered

sub-structures with spatial frequencies fi¼ i�DfDG, where iis the number of diffraction order.

The theoretical modeling of light diffraction is shown

for single periodical structure with N¼ 3. However, the real

surface of epitaxial film is the ensemble of ordered but dif-

ferent in shape VO2 grains. This system has noticeable sto-

chastic component that contributes to the scattering

indicatrix, resulting in slight difference between positions of

some diffraction peaks obtained experimentally and from

theoretical calculation [Fig. 8(b)].

Despite similar scattering indicatrices for 30-nm- and

125-nm-thick films VO2/Al2O3(r-cut) [Figs. 1(a) and 8(a)],

there is considerable difference in their temperature-

dependent structural transformation. The BSDF(f) of the

thinner film shows significant qualitative change at different

temperatures (Figs. 1(a) and 4), but the 125-nm-thick film

shows almost uniform decay of diffraction peaks withoutany significant shift or distortion [Fig. 8(b)]. When VO2 is

switched into its metallic phase, the local BSDF(f) maxima

are suppressed at T¼ 373 K, but their positions remain the

same. This indicates that the domain pattern of the 125-nm-

thick film remains also the same, and no additional twinning

or “dynamic” temperature-dependent reorganization of

domains occurs. It is very likely that the static domain struc-

ture is formed during the PLD process via generation of the

dislocation network and introduction of new grain bounda-

ries or microcracks.

The VO2 PLD film on r-cut Al2O3 substrate is mis-

matched, with misfit strain �m¼ 4.0% along [010]VO2 and

�m¼�5.1% along [001]VO2.41 If the thickness is smaller

than the critical value hc, the film is maximally strained but

free of MDs.68,69 However, when the thickness exceeds the

threshold hc, the MD network abruptly appears to reduce the

misfit strain. Data obtained for the 125-nm-thick VO2/

Al2O3(r-cut) film indicate that the thickness of this film is

above hc. Thus, the PLD at T¼ 825 K has formed a flat epi-

taxial film in tetragonal phase with relatively high concentra-

tion of MDs. It is also very likely that when the film is

cooled down to room temperature after the deposition, differ-

ent thermal expansion of the film and substrate along with

the VO2 volume contraction by �0.044% (Ref. 60) resulted

in additional generation of dislocations, new grain bounda-

ries, or microcracks with self-organization of VO2 domains

into periodical structures. Once generated, the network of

structural defects then significantly contributes to the PT pro-

cess. These defects prevent a “dynamic” temperature-

dependent twinning of 125-nm-thick film during the PT, as

compared to the thinner film. As a result, sharp BSDF(f)peaks in scattering indicatrix do not shift, but decay as tem-

perature increases [Fig. 8(b)].

As shown previously for VO2/Si samples prepared by

RF sputtering,22 the absolute value of residual stress drops

by more than nine times, as the film thickness increases from

100 nm to 440 nm. For the epitaxial VO2/Al2O3(r-cut) PLD

films, the strain and stress both are noticeably suppressed al-

ready for 125-nm-thick film due to introduction of structural

defects, as revealed from the evolution of scattering pattern

in Fig. 8(b). The alteration of the stress during the PT is

small enough and insufficient to produce the film twinning

or formation of new domains.

The relative change of the scattering signal allows to

identify spatial frequencies of VO2 domains with different PT

properties. Thus, the DBSDF(T)/BSDF0 indicatrix in Fig. 9(a)

FIG. 8. Light scattering by 125-nm-thick film VO2/Al2O3(r-cut). (a) Scattering indicatrices for insulating and metallic phases. (b) Cross-section of BSDF indi-

catrix. IDG is the simulated diffraction intensity for diffraction grating with N¼ 3, d¼ 12 lm, and s¼ 0.61 lm. (Multimedia view) [URL: http://dx.doi.org/

10.1063/1.4921057.3]

184304-8 Lysenko et al. J. Appl. Phys. 117, 184304 (2015)

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can be divided into three regions: Df1¼ 1.15–1.58 lm�1 (size

range is 0.633–0.870 lm), Df2¼ 0.7–1.15 lm�1 (size range is

0.870–1.43 lm), and region with f< 0.7 lm�1 (d> 1.43 lm).

Near the PT point, at T¼ 336 K, the scattering signal drops

uniformly within the region Df1 with higher rate. As the tem-

perature approaches T¼ 341 K, the signal continuously

decreases, but with noticeably different rate for each region,

indicating different PT dynamics for domains of different

size.

The VO2/Al2O3 films used in this study are epitaxial and

nearly stoichiometric, but their different microstructure sig-

nificantly affects the thermal hysteresis. The hysteresis loop

of optical transmittance and integrated light scattering for

the 125-nm-thick film [Figs. 9(b) and 9(c)] is much broader

and significantly tilted as compared to the hysteresis of the

thinner film [see Fig. 7(a)]. This difference is attributed to

the higher concentration of structural defects in the 125-nm-

thick film. As was discussed above, the strain field in this

film is significantly reduced due to high density of MDs.

Therefore, the broad and tilted hysteresis in Figs. 9(b) and

9(c) has no significant relation to the strain but rather to the

presence of defects. The structural defects shift the PT tem-

perature. During the PT, some domain walls are pinned by

defects, contributing to the distortion of the hysteresis shape

and width.

The hysteresis of optical transmittance ITR/I0 does not

coincide exactly with that of integrated light scattering Iscatt/

I0 [Figs. 9(b) and 9(c)], since the scattered light is addition-

ally affected by structural and dielectric constant inhomoge-

neity. Hysteresis loops I�scatt=I0 show significant grain-size-

dependence. Using the derivatives dI�scatt=dT [Fig. 9(d)], the

characteristic hysteresis width for f¼ 0.62 lm�1 is found to

be DT¼ 19.5 K. However as soon as spatial frequency

exceeds 0.7 lm�1, the hysteresis width shrinks to DT¼ 5 K

and weakly depends on f. Along with narrowing of hystere-

sis, the second principal feature of Fig. 9(c) is a gradual shiftof the hysteresis loop with its steeper slope to higher f, as the

spatial frequency increases. Here, at the higher spatial fre-

quency f¼ 1.4 lm�1, the hysteresis width and position

remarkably approaches those values related to thinner film

[see Fig. 7(a)], indicating similar physical properties of the

30-nm-thick film and grains of the 125-nm-thick film with

f¼ 1.4 lm�1.

The observed behavior of hysteresis loops for different

spatial frequencies evidences a gradual size-dependent

change of structural parameters. The MD network is assumed

as the main origin which affects the thermal hysteresis. The

broad hysteresis DT¼ 19.5 K for f< 0.7 lm�1 and its abrupt

change to DT ’ 5 K above f¼ 0.7 lm�1 [see Fig. 9(d), inset]

indicates that the larger structures with f< 0.7 lm�1 contain

higher densities of MDs. The pining of domain walls by

defects changes the tilt of the hysteresis loop and possibly is

the origin of the second minimum in the dI�scatt=dT curve

for f¼ 0.62 lm�1. The significant change of the hysteresis

width and slope at f¼ 0.7 lm�1 indicates a possible presence

of a “transverse” threshold for the generation of MDs at this

spatial frequency. Above f¼ 0.7 lm�1 the concentration of

MDs rapidly drops and continuously decreases for smaller

grains. Thus, already at f¼ 1.4 lm�1, the hysteresis loop of

the 125-nm-thick film approaches in shape that of the 30-nm-

thick film, which is almost free of MDs.

CONCLUSION

In this paper, the influence of strain and structural

defects on thermally induced PT of epitaxial VO2/Al2O3

films has been discussed. The angle-resolved light scattering

measurements show that the elastic stain significantly affects

the thermal transition, resulting in temperature-dependent

twinning of microcrystallites and domain formation at tem-

peratures much below the PT point Tc. The scattering indica-

trix, surface power spectral density, and autocorrelation

function demonstrate distinctive qualitative change during

the transition. At the critical temperature Tc, disorder of the

30-nm-thick film reaches the highest level due to coexistence

of insulating and metallic phases. Here, the surface autocor-

relation length drops to its minimal value. However, when

FIG. 9. Optical properties of 125-nm-thick VO2/Al2O3(r-cut) film near the

PT point. (a) The relative change of scattering signal at T¼ 336 K and

T¼ 341 K. (b) Hysteretic evolution of transmittance at k¼ 1310 nm. (c)

Scattering signal Iscatt/I0 integrated within hemisphere and signal I�scatt for

different spatial frequencies of the surface. (d) Derivative of the hysteresis

curves. Inset shows location of dI�scatt=dT minima versus spatial frequency.

184304-9 Lysenko et al. J. Appl. Phys. 117, 184304 (2015)

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VO2 switches into metallic state, the autocorrelation length

recovers back, close to its initial value in the insulating

phase. As the film switches from M1 to R-phase, the fractal

dimension of the surface decreases, indicating smother sur-

face with more uniform optical properties in the metallic

phase. It is shown that the hysteresis loop depends on spatial

frequency of surface irregularities. Smaller grains of 30-nm-

thick film have broader hysteresis and noticeable “transition

opalescence” due to higher elastic strain and higher concen-

trations of point defects.

When the film thickness exceeds the threshold value for

the introduction of misfit dislocations, these dislocations

noticeably suppress the internal strain in the film. Thus, the

strain in relatively thick 125-nm film is substantially

reduced, showing considerably different light scattering and

structural evolution upon thermally induced PT, as compared

to the strained 30-nm-thick film with lower concentration of

misfit dislocations. The broadening of the hysteresis loop

increases with concentration of dislocations, since domain

walls of a new phase are pinned by defects. In the absence of

internal strain, the BSDF scattering pattern does not change

qualitatively with temperature, indicating the absence of

temperature-dependent film twinning or formation of new

domain pattern.

The considerably different evolution of the scattering

indicatrix for the films with higher internal elastic strain and

for thicker films where this strain is suppressed by misfit dis-

locations opens new possibilities for selection and classifica-

tion of these films by angle-resolved light scattering

technique.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the support from

UPRM College of Arts and Sciences. N.S. was supported in

part by the National Science Foundation under Grant No.

ECCS-1139773.

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